The financial return of equity-indexed annuities depends on an underlying fund or investment portfolio complemented by an investment guarantee. We discuss a so-called cliquet-style or ratchet-type guarantee granting a minimum annual return. Its path-dependent payoff complicates valuation and risk management, especially if interest rates are modelled stochastically. We develop a novel scenario-matrix (SM) method. In the example of a Vasicek-Black-Scholes model, we derive closed-form expressions for the value and moment-generating function of the final payoff in terms of the scenario matrix. This allows efficient evaluation of values and various risk measures, avoiding Monte-Carlo simulation or numerical Fourier inversion. In numerical tests, this procedure proves to converge quickly and outperforms the existing approaches in the literature in terms of computation time and accuracy.

股票指数年金的财务回报取决于基础基金或投资组合并辅以投资担保。我们讨论所谓的“集团式”或“棘轮式”担保，授予最低年回报率。其路径依赖的回报使估值和风险管理变得复杂，特别是在利率随机建模的情况下。我们开发了一种新颖的场景矩阵（SM）方法。在 Vasicek-Black-Scholes 模型的示例中，我们根据场景矩阵推导了最终收益的值和矩生成函数的封闭式表达式。这可以有效评估价值和各种风险度量，避免蒙特卡罗模拟或数值傅里叶反演。在数值测试中，该过程证明可以快速收敛，并且在计算时间和准确性方面优于文献中的现有方法。